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Probably not the correct place for this, but the swimmer description of this derivative wrt lake temperature was wonderful and *really* clarified this for me. Thank you! 133.87.57.32 ( talk) 13:06, 23 June 2012 (UTC)
Am I confused, or does this article change notation between the introduction and the proof? Is D/Dt the same operator as d/dt? Tom Duff 19:19, 30 January 2006 (UTC)
Also, what does the hat on the B in the "proof" section refer to? A hat can have many meanings, there should be a line saying "where B-hat indicates that [whatever it indicates]" 140.184.21.115 13:35, 19 September 2007 (UTC)
Looks to me like this article ought to be rolled in with substantive derivative. Linuxlad 14:19, 22 June 2006 (UTC)
The identity given for taking the material derivative of an integral is the Reynolds Transport Theorem, though written in a form that is dissimilar to the one listed in the article concerning that theorem. This is also a varient of the Liebnitz Rule.
Is there any special reason for the parentheses used on the RHS in the definitions? —DIV ( 128.250.204.118 09:04, 6 April 2007 (UTC))
Assume that
By the chain rule
dividing both side by , we get
since , and , the above equation becomes
Hence, we see that and are one and the same. Therefore, the substantial derivative is nothing more than a total derivative with respect to time. The only advantage of the substantial derivative notation is that it higlights more of the physical significance (time rate of change following a moving fluid element).
I think that the terminology "substantial derivative" and "total derivative" are unnecessarilly confusing (As far as I know, this terminology is mainly prevalent in fluid dynamics) The wikipedia article should explain that they are different way to express the same thing.
199.212.17.130 13:47, 31 August 2007 (UTC)
The first section of this article claims to define the convective derivative. The next section offers a proof. How can a definition be proven? I am confused. Is the proof intended to show that the convective derivative is the partial derivative with respect to time in a frame that moves with material particles? That requires some reasoning, I think, not just direct application of the chain rule.
155.37.79.216 14:27, 7 September 2007 (UTC)
If and only if is a Lagrangian point, so , does the total time derivative equal the convective derivative.
139.80.48.19 ( talk) 22:29, 19 March 2008 (UTC)
I propose to rename this article to Material derivative, because:
phrase | hits |
---|---|
material derivative | 837 |
substantial derivative | 693 |
convective derivative | 650 (incl. uses for only the spatial part) |
Lagrangian derivative | 490 |
substantive derivative | 407 |
derivative following the motion | 321 |
particle derivative | 177 |
hydrodynamic derivative | 162 |
Stokes derivative | 106 |
advective derivative | 77 |
Crowsnest ( talk) 22:26, 23 June 2008 (UTC)
According to Help:Section#Floating_the_TOC, the TOC is floated "when it is beneficial to the layout of the article, or when the default TOC gets in the way of other elements." In what way is the template here beneficial to the layout of the article? More than 99% of our mathematics articles have never used this template; many of them have identical layouts of a lede section, a TOC, and then several lower sections, without images or other floating elements. — Carl ( CBM · talk) 18:13, 21 May 2010 (UTC)
I agree. I've read a lot of science, engineering and maths articles, and never seen this layout before. I didn't even see the t.o.c. until reading this talk page entry. Michael Hodgson ( talk) 07:30, 25 October 2021 (UTC)
I want to ask if the formula for the material derivative for vector fields is wrong: it does not seem to define an objective quantity. I would have strongly expected an additional corotational term $+\vec{\omega} \times \vec{A}$, where $\vec{\omega}$ is the local vorticity of the fluid, because a rotating flow should rotate any local vectorial quantity $\vec{A}$ associated with the material. In the literature, this material derivative for vectorial quantities (including the additional corrotation term) is sometimes referred to as Jaumann corotational derivative if I understand correctly.
I would like to change the main article, but want to consult with the community first. Benjamin.friedrich ( talk) — Preceding undated comment added 09:09, 16 January 2021 (UTC)
![]() | This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||||
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Probably not the correct place for this, but the swimmer description of this derivative wrt lake temperature was wonderful and *really* clarified this for me. Thank you! 133.87.57.32 ( talk) 13:06, 23 June 2012 (UTC)
Am I confused, or does this article change notation between the introduction and the proof? Is D/Dt the same operator as d/dt? Tom Duff 19:19, 30 January 2006 (UTC)
Also, what does the hat on the B in the "proof" section refer to? A hat can have many meanings, there should be a line saying "where B-hat indicates that [whatever it indicates]" 140.184.21.115 13:35, 19 September 2007 (UTC)
Looks to me like this article ought to be rolled in with substantive derivative. Linuxlad 14:19, 22 June 2006 (UTC)
The identity given for taking the material derivative of an integral is the Reynolds Transport Theorem, though written in a form that is dissimilar to the one listed in the article concerning that theorem. This is also a varient of the Liebnitz Rule.
Is there any special reason for the parentheses used on the RHS in the definitions? —DIV ( 128.250.204.118 09:04, 6 April 2007 (UTC))
Assume that
By the chain rule
dividing both side by , we get
since , and , the above equation becomes
Hence, we see that and are one and the same. Therefore, the substantial derivative is nothing more than a total derivative with respect to time. The only advantage of the substantial derivative notation is that it higlights more of the physical significance (time rate of change following a moving fluid element).
I think that the terminology "substantial derivative" and "total derivative" are unnecessarilly confusing (As far as I know, this terminology is mainly prevalent in fluid dynamics) The wikipedia article should explain that they are different way to express the same thing.
199.212.17.130 13:47, 31 August 2007 (UTC)
The first section of this article claims to define the convective derivative. The next section offers a proof. How can a definition be proven? I am confused. Is the proof intended to show that the convective derivative is the partial derivative with respect to time in a frame that moves with material particles? That requires some reasoning, I think, not just direct application of the chain rule.
155.37.79.216 14:27, 7 September 2007 (UTC)
If and only if is a Lagrangian point, so , does the total time derivative equal the convective derivative.
139.80.48.19 ( talk) 22:29, 19 March 2008 (UTC)
I propose to rename this article to Material derivative, because:
phrase | hits |
---|---|
material derivative | 837 |
substantial derivative | 693 |
convective derivative | 650 (incl. uses for only the spatial part) |
Lagrangian derivative | 490 |
substantive derivative | 407 |
derivative following the motion | 321 |
particle derivative | 177 |
hydrodynamic derivative | 162 |
Stokes derivative | 106 |
advective derivative | 77 |
Crowsnest ( talk) 22:26, 23 June 2008 (UTC)
According to Help:Section#Floating_the_TOC, the TOC is floated "when it is beneficial to the layout of the article, or when the default TOC gets in the way of other elements." In what way is the template here beneficial to the layout of the article? More than 99% of our mathematics articles have never used this template; many of them have identical layouts of a lede section, a TOC, and then several lower sections, without images or other floating elements. — Carl ( CBM · talk) 18:13, 21 May 2010 (UTC)
I agree. I've read a lot of science, engineering and maths articles, and never seen this layout before. I didn't even see the t.o.c. until reading this talk page entry. Michael Hodgson ( talk) 07:30, 25 October 2021 (UTC)
I want to ask if the formula for the material derivative for vector fields is wrong: it does not seem to define an objective quantity. I would have strongly expected an additional corotational term $+\vec{\omega} \times \vec{A}$, where $\vec{\omega}$ is the local vorticity of the fluid, because a rotating flow should rotate any local vectorial quantity $\vec{A}$ associated with the material. In the literature, this material derivative for vectorial quantities (including the additional corrotation term) is sometimes referred to as Jaumann corotational derivative if I understand correctly.
I would like to change the main article, but want to consult with the community first. Benjamin.friedrich ( talk) — Preceding undated comment added 09:09, 16 January 2021 (UTC)